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Compared with aeromagnetic total-field data, aeromagnetic vertical gradient field data contain less low-frequency information. In this paper, a continuation conversion filtering algorithm is proposed to filter out part of the low-frequency information of the aeromagnetic total-field data so that these data can be better compared with the total-field data obtained from aeromagnetic gradient data conversion. We discuss the feasibility of single aeromagnetic vertical gradient measurement in areas where it is inconvenient to erect base stations. We design a simple model and a complex model with a background field and random noise to analyze the conversion effect. The model analysis shows that the effect of applying the algorithm depends heavily on the selection of upward continuation height. The magnetization intensity of the background field also affects the selection of continuation height. When the magnetization intensity of the background field is weak, the continuation height chosen is the same as the buried depth of the background field. If the magnetization intensity of the background field is strong, then the higher the continuation height, the better the effect will be. The conclusion of the model analysis is applied to the analysis of the measured aeromagnetic data. In addition, we can conclude that the effect on total-field data of conversion by the continuation conversion filtering algorithm is better than that of conversion from the aeromagnetic vertical gradient data. [ABSTRACT FROM AUTHOR]

Distribution system state estimation (DSSE) is an essential tool for the management and control of future distribution networks. Distribution grids are usually characterized by a very large number of nodes and different voltage levels. Moreover, different portions of the system can be operated by different distribution system operators. In this context, multiarea approaches are key tools to efficiently perform DSSE. This paper presents a novel approach for multiarea state estimation in distribution systems. The proposed algorithm is based on a two-step procedure, where the first-step local estimations are refined through a newly designed second step that allows the integration of the measurement information available in the adjacent areas. The main novelty in this paper is the mathematical analysis of the impact brought by possible measurements shared among different areas, which drives the design of a new efficient weighted least squares formulation of the second step to maximize the achievable estimation accuracy. Tests performed on the unbalanced IEEE 123-bus network prove the goodness of the new multiarea estimator proposed and show the accuracy and efficiency enhancements obtainable with respect to previous literature. [ABSTRACT FROM PUBLISHER]

Most of the proposed methods for investigating the transient and short-term voltage (STV) stability have assumed that only one of the two phenomena exists, i.e. either transient instability or STV instability. While these two phenomena exist simultaneously with one of them being dominant, according to the operating point of the system and disturbance condition. A unified online prediction method is presented in this paper to distinguish between the stable and unstable conditions. In the proposed method, by employing the intelligent wide area measurement system (IWAMS), the frequency deviation and the active power imbalance are calculated by the generation buses, which are considered as the intelligent generation buses (IGB). By tracking the trajectories of the frequency deviation and the active power imbalance and checking some simple defined rules, early prediction of both transient and STV instability can be achieved. In order to evaluate the performance of the proposed algorithm, the method has been tested on single machine infinite bus (SMIB) system, single machine load bus (SMLB) system, IEEE 39-bus system and IEEE 118-bus system. According to the obtained results, the proposed algorithm has the overall accuracy of 99.5% under symmetrical and asymmetrical faults, PMU measurement error, different operating points and topological changes. [ABSTRACT FROM AUTHOR]

The determination of the optimal measurement area of the articulated arm measuring machine belongs to the multi-dimensional function optimization problem under complex constraints. To realize high-precision measurement of low-precision articulated arm measuring machine, we analyze the working principle and error source of the measuring machine, and establish the optimization target model of the optimal measurement area in this paper. We propose a method for determining the optimal measurement area of an articulated arm measuring machine based on improved FOA. The basic FOA algorithm is improved, the historical optimal individual and population centroid information are added in the population iteration update process, and the fruit fly individuals in each iteration are directly used as the taste concentration judgment value, which increases cooperation and information sharing among fruit fly individuals, and improves the global optimization ability and stability of the algorithm. In the designated area of the measuring machine, we have carried out comparative experiments on the optimization results of improved FOA and basic FOA, ACO, PSO, AL-SC-FOA, LGMS-FOA, IPGS-FFO. Experimental results show that the improved FOA, ACO, PSO, and IPGS-FFO algorithms do not fall into local optimum, and the optimal measurement area determined by them is consistent with the optimization results of other algorithms, and is superior to other algorithms in convergence speed and stability, so it is more suitable for determining the optimal measurement area of articulated arm measuring machine. [ABSTRACT FROM AUTHOR]

Fastener assembly is a tedious and time-consuming work because operators have to check assembly manuals and find right fastener for each hole. Hence, this paper aims to develop a three-dimensional (3-D) projection system that projects assembly instruction onto the work piece surface directly to guide operators to assemble. However, in order to project the instruction accurately, the corresponding part of the computer-aided design model of the physical scanned area needs to be attained through the rapid and accurate registration. In order to achieve this goal, first, a high-accuracy and rapid 3-D measurement system is developed; second, a fast registration method based on local multiscale geometric feature vector is proposed to accelerate the registration speed and improve the registration reliability. Experimental results demonstrate the measurement accuracy of the developed system, and verify the feasibility of the proposed registration method. Hence, the proposed method can lead to improved assembly efficiency and decreased error probability, making great contributions to large-scale structure assembly. [ABSTRACT FROM PUBLISHER]

In this paper, we will study floorplanning in 3-D integrated circuits (3D-ICs). Although literature is abundant on 3D-IC floorplanning, none of them consider the areas and positions of signal through-silicon vias (TSVs). In previous research, signal TSVs are viewed as points during the floorplanning stage. Ignoring the areas, positions and connections of signal TSVs, previous research estimates wirelength by measuring the half-perimeter wirelength of pins in a net only. Experimental results reveal that 29.7% of nets possess signal TSVs that cannot be put into the white space within the bounding boxes of pins. Moreover, the total wirelength is underestimated by 26.8% without considering the positions of signal TSVs. The considerable error in wirelength estimation severely degrades the optimality of the floorplan result. Therefore, in this paper, we will propose a two-stage 3-D fixed-outline floorplaning algorithm. Stage one simultaneously plans hard macros and TSV-blocks for wirelength reduction. Stage two improves the wirelength by reassigning signal TSVs. Experimental results show that stage one outperforms a post-processing TSV planning algorithm in successful rate by 57%. Compared to the post-processing TSV planning algorithm, the average wirelength of our result is shorter by 22.3%. In addition, stage two further reduces the wirelength by 3.45% without any area overhead. [ABSTRACT FROM AUTHOR]

This paper proposes a parametric, statistical model for adapting the load-frequency-control (LFC) target values that are used for a performance evaluation. These target values should be determined in such a way that the system frequency will be bounded within the target range. One way of bounding the system frequency is to bound the variations of the area-control error (ACE) by increasing the control activations. On the other hand, the frequency can also be bounded by mutual coordination of the control among the control areas, thus affecting the covariances between the ACEs. Existing models for determining the LFC target values do not consider the covariances between the ACEs. The proposed model incorporates, for each area individually, the estimated value of the covariances between the ACEs and is inherently frequency dependent. In this way, appropriate shares are obtained for the target ACE ranges among the control areas. The extensive field measurements in the discussed control area confirm the advantages of the proposed model over existing models for a monthly and online estimation of the LFC target values. [ABSTRACT FROM AUTHOR]

The introduction of wide area measurements has brought a need for real time assessment methods of power systems, which are accurate and fast. The time varying coefficients in synchronous machine equations make it difficult to find solutions to obtain machine voltages, currents and flux linkages when expressed in phase quantities under transient conditions. The paper presents an approach to design power system transient stability assessment using direct methods for a multi-machine network based on multiple synchronized phasors, measured from Phasor Measurement Units (PMUs) and generator parameters. The generator rotor angle was derived from phasor measurements of voltage and current, and generator parameters using direct algorithm . The method assumes that a temporary fault is applied to the system therefore the pre-fault and post-fault conditions are similar. The multi-machine system was reduced to groups denoted Single Machine to Equivalent Bus (SMEB) models and another groups denoted Load Equivalent Bus (LEB) using Parallel Algorithms (PAs) [1]. The use of these PAs eliminates the SPMUs at each bus in the system, and it is required number of SPMUs only equals the number of generator buses. So that, the Equal Area Criterion in both rotor angle domain and time domain can be applicable for the SMEBs groups to assess the system stability in real-time through the Synchro-Phasors Measurements Units (SPMUs). A temporary three phase fault was simulated at test system comprises 2-machine, 8-bus network for validating the novel algorithm. [ABSTRACT FROM AUTHOR]

This paper proposes a decentralized state-estimation approach that relies on an elaborated instance of the Lagrangian relaxation decomposition technique. The proposed algorithm does not require a central coordinator but just to moderate interchanges of information among neighboring regions, and exploits the structure of the problem to achieve a fast and accurate convergence. Additionally, a decentralized bad measurement identification procedure is developed, which is efficient and robust in terms of identifying bad measurements within regions and in border tie-lines. The accuracy and efficiency of the proposed procedures are assessed by a large number of simulations, which allows drawing statistically sound conclusions. [ABSTRACT FROM PUBLISHER]

Reading the doctoral thesis of Napp Avelli (2007) I realized that Gabriel's localization theory, which I applied in context with the stabilization of multidimensional input/output behaviors, can also be used for the construction of regular almost interconnections of behaviors in arbitrary dimensions and not only in two dimensions. In this paper I expose this theory in the language of quotient modules and derive an algorithm for arbitrary dimensions which has, however, not yet been implemented. Regular interconnections were introduced and discussed by Willems [IEEE Trans. Automat. Control, 36 (1991), pp. 259-294; 42 (1997), pp. 458-472] for one-dimensional behaviors. Their multidimensional counterparts have been treated by Rocha, Wood, Shankar, Zerz, Lomadze, Napp Avelli, and others since 1998. Two-dimensional almost direct sum decompositions and regular almost interconnections have been considered by Valcher and Bisiacco since 2000 and are also the main subject of Napp Avelli's thesis and his recent submitted paper. Roughly, two behaviors are almost equal if they differ by finite-dimensional behaviors only; so the latter are considered negligible in this context. Two-dimensional behaviors have special properties which are not discussed in the present paper. I also briefly discuss other variants of regular almost interconnections where only stable autonomous behaviors are considered negligible. [ABSTRACT FROM AUTHOR]

Phenotypic characteristics of fruit particles, such as projection area, can reflect the growth status and physiological changes of grapes. However, complex backgrounds and overlaps always constrain accurate grape border recognition and detection of fruit particles. Therefore, this paper proposes a two-step phenotypic parameter measurement to calculate areas of overlapped grape particles. These two steps contain particle edge detection and contour fitting. For particle edge detection, an improved HED network is introduced. It makes full use of outputs of each convolutional layer, introduces Dice coefficients to original weighted cross-entropy loss function, and applies image pyramids to achieve multi-scale image edge detection. For contour fitting, an iterative least squares ellipse fitting and region growth algorithm is proposed to calculate the area of grapes. Experiments showed that in the edge detection step, compared with current prevalent methods including Canny, HED, and DeepEdge, the improved HED was able to extract the edges of detected fruit particles more clearly, accurately, and efficiently. It could also detect overlapping grape contours more completely. In the shape-fitting step, our method achieved an average error of 1.5% in grape area estimation. Therefore, this study provides convenient means and measures for extraction of grape phenotype characteristics and the grape growth law. [ABSTRACT FROM AUTHOR]

In this paper, a joint probabilistic data association algorithm based on loss function (LJPDA) is proposed so that the computation load and accuracy of the multi-target tracking algorithm can be guaranteed simultaneously. Firstly, data association is divided in to three cases based on the relationship among validation gates and the number of measurements in the overlapping area for validation gates. Also the contribution coefficient is employed for evaluating the contribution of a measurement to a target, and the loss function, which reflects the cost of the new proposed data association algorithm, is defined. Moreover, the equation set of optimal contribution coefficient is given by minimizing the loss function, and the optimal contribution coefficient can be attained by using the Newton-Raphson method. In this way, the weighted value of each target can be achieved, and the data association among measurements and tracks can be realized. Finally, we compare performances of LJPDA proposed and joint probabilistic data association (JPDA) algorithm via numerical simulations, and much attention is paid on real-time performance and estimation error. Theoretical analysis and experimental results reveal that the LJPDA algorithm proposed exhibits small estimation error and low computation complexity. [ABSTRACT FROM AUTHOR]

This paper introduces a new algorithm (BUNTUS—Built-up, Nighttime Light, and Travel time for Urban Size) using remote sensing techniques to delineate urban boundaries. The paper is part of a larger study of the role of urbanisation in changing fossil fuel emissions. The method combines estimates of land cover, nighttime lights, and travel times to classify contiguous urban areas. The method is automatic, global and uses data sets with enough duration to establish trends. Validation using ground truth from Landsat-8 OLI images revealed an overall accuracy ranging from 60% to 95%. Thus, this approach is capable of describing spatial distributions and giving detailed information of urban extents. We demonstrate the method with examples from Brisbane, Australia, Melbourne, Australia, and Beijing, China. The new method meets the criteria for studying overall trends in urban emissions. [ABSTRACT FROM AUTHOR]

The effective and accurate area measurement of body surface injury regions is important for the appraisal work of forensic medicine of public security. Considering that most of the area measurement methods used in current forensic appraisals still have strong dependence on man-made manipulation, a fuzzy c-means (FCM)-based area measurement system for body surface injury regions is designed in this paper. Aiming at the problems of poor clustering effects and poor real-time performance of FCM in the area measurement process, a design method based on super-pixel segmentation and multi-subgroup parallel artificial fish swarm is proposed in the designed system, and on this basis, the overall process framework and system workflow are designed and given. Finally, the simulation results show that the designed system can effectively improve the segmentation quality, segmentation speed, and area measurement precision of the injury region, thus providing better effectiveness and accuracy for the appraisal work of forensic medicine. [ABSTRACT FROM AUTHOR]

Controlled islanding is the last countermeasure for a bulk power system when it suffers from severe cascading contingencies. The objective of controlled islanding is to maintain the stability of each island and to keep the total loss of loads of the whole system to a minimum. This paper presents a novel integrated wide-area measurement systems (WAMS)-based adaptive controlled islanding strategy, which depends on the dynamic post-fault trajectories under different failure modes. We first utilize an improved Laplacian eigenmap algorithm (ILEA) to identify the coherent generators and use the slow coherency grouping algorithm to guarantee coherent stability within an island. Using the identification result, we then define the minimum coherent generator virtual nodes to reduce the searching space in a graph and utilize the k-way partitioning (KWP) algorithm to obtain a preliminary partition of the simplified graph. Based on the preliminary partition, we consider the direction of power flow and propose a variable neighborhood heuristic searching algorithm to search the optimal separation surfaces so that the net imbalanced power of islands is minimized. Finally, the bidirectional power flow tracing algorithm and PQ decomposition power flow analysis are utilized to determine the corrective controls within each island. The test results with the New England 39-bus system and the IEEE 118-bus system show that the proposed integrated controlled islanding strategy can automatically adapt to different fault modes through generator coherency identification and effectively group the different coherent generators into different islands. [ABSTRACT FROM AUTHOR]

This paper presents results of a technique developed to measure the volume and the surface area of flaws in pin-type polymer insulators used in electrical energy distribution networks by means of computed tomography (CT). The tomography images were reconstructed using 180 digital radiographs (projections) acquired from a high-resolution system (a 50 μm × 50 μm, a-Si pixel detector). An acrylic phantom containing 12 cylindrical holes of known volume was used to test the tomography measurement system. In order to improve the quality of tomography images, two procedures were used, namely, ‘subtraction of dark image’ and ‘correction of light field’, as well as a sequence of filters such as the median and the Gaussian. Image processing techniques were used for the segmentation of flaws in the CT images. The Marching Cubes algorithm was used in the visualisation process and the Decimation algorithm was used to obtain volume and surface area measurements of flaws. The programs were developed in C++ and Java, using the VTK – Visualisation Toolkit library. The results obtained showed to be satisfactory for quantitatively and qualitatively analysing the effects of electrical discharges in insulation materials such as insulators and cables. [ABSTRACT FROM AUTHOR]

This paper proposes a technique for partitioning a large power system into a number of coherent electric areas for possible application to dynamic vulnerability assessment. The coherency concept and a fuzzy clustering algorithm grouping of buses are combined to achieve this goal. The clusters are obtained by selecting representative buses from the data set in such a way that the total fuzzy dissimilarity within each cluster is minimized. The initialization problem of the conventional Fuzzy c-means algorithm, which usually leads to multiple solutions, is suitably tackled by incorporating the maximum-dissimilarity based sequential Phasor Measurement Unit (PMU) placement technique. Results of bus grouping for two test systems of three and nine areas demonstrate the potential of the approach. It is observed that such an approach to bus grouping results in a PMU configuration with minimum number of devices and fast data aggregation for a wide-area measurement system. [ABSTRACT FROM AUTHOR]

Wireless access points (APs) divide a plane into small areas where their coverage ranges overlap. A mobile device can be located within a particular small overlapped area based on the unique set of APs covering the device. We formally define an Optimal Loc-deployment problem for both coverage and area localization. Our objective is to deploy a minimum number of APs that provide full communication coverage while achieving the ability to locate a mobile device within a certain area no larger than a given accuracy parameter. We obtain a formula that precisely determines the optimal solution for more than half of the accuracy values. For the rest of the accuracy values, we propose an algorithm that will return an approximation whose difference to the optimal solution is less than \epsilon for any \epsilon > 0. Finally, we conduct extensive numerical evaluation and real experiments to validate our proposed solutions. [ABSTRACT FROM PUBLISHER]

Abstract: For a set of n points in the plane, we consider the axis-aligned -Box Covering problem: Find p axis-aligned, pairwise-disjoint boxes that together contain at least points. In this paper, we consider the boxes to be either squares or rectangles, and we want to minimize the area of the largest box. For general p we show that the problem is NP-hard for both squares and rectangles. For a small, fixed number p, we give algorithms that find the solution in the following running times: For squares we have time for , and time for . For rectangles we get for and time for . In all cases, our algorithms use space. [ABSTRACT FROM AUTHOR]

The state estimation algorithm estimates the values of the state variables based on the measurement model described as the system of equations. Prior to applying the state estimation algorithm, the existence and uniqueness of the solution of the underlying system of equations is determined through the observability analysis. If a unique solution does not exist, the observability analysis defines observable islands and further defines an additional set of equations (measurements) needed to determine a unique solution. For the first time, we utilise factor graphs and Gaussian belief propagation algorithm to define a novel observability analysis approach. The observable islands and placement of measurements to restore observability are identified by following the evolution of variances across the iterations of the Gaussian belief propagation algorithm over the factor graph. Due to sparsity of the underlying power network, the resulting method has the linear computational complexity (assuming a constant number of iterations) making it particularly suitable for solving large-scale systems. The method can be flexibly matched to distributed computational resources, allowing for determination of observable islands and observability restoration in a distributed fashion. Finally, we discuss performances of the proposed observability analysis using power systems whose size ranges between 1354 and 70 000 buses. [ABSTRACT FROM AUTHOR]

Measurement of total-plaque-area (TPA) is important for determining long term risk for stroke and monitoring carotid plaque progression. Since delineation of carotid plaques is required, a deep learning method can provide automatic plaque segmentations and TPA measurements; however, it requires large datasets and manual annotations for training with unknown performance on new datasets. A UNet++ ensemble algorithm was proposed to segment plaques from 2D carotid ultrasound images, trained on three small datasets (n = 33, 33, 34 subjects) and tested on 44 subjects from the SPARC dataset (n = 144, London, Canada). The ensemble was also trained on the entire SPARC dataset and tested with a different dataset (n = 497, Zhongnan Hospital, China). Algorithm and manual segmentations were compared using Dice-similarity-coefficient (DSC), and TPAs were compared using the difference (Δ TPA), Pearson correlation coefficient (r) and Bland-Altman analyses. Segmentation variability was determined using the intra-class correlation coefficient (ICC) and coefficient-of-variation (CoV). For 44 SPARC subjects, algorithm DSC was 83.3–85.7%, and algorithm TPAs were strongly correlated (r = 0.985–0.988; p < 0.001) with manual results with marginal biases (0.73–6.75) mm2 using the three training datasets. Algorithm ICC for TPAs (ICC = 0.996) was similar to intra- and inter-observer manual results (ICC = 0.977, 0.995). Algorithm CoV = 6.98% for plaque areas was smaller than the inter-observer manual CoV (7.54%). For the Zhongnan dataset, DSC was 88.6% algorithm and manual TPAs were strongly correlated (r = 0.972, p < 0.001) with $\Delta$ TPA = −0.44 ± 4.05 mm2 and ICC = 0.985. The proposed algorithm trained on small datasets and segmented a different dataset without retraining with accuracy and precision that may be useful clinically and for research. [ABSTRACT FROM AUTHOR]

Jet production in lead-lead (PbPb) and proton-proton (pp) collisions at a nucleon-nucleon center-of-mass energy of 5.02 TeV is studied with the CMS detector at the LHC, using PbPb and pp data samples corresponding to integrated luminosities of 404 μb−1 and 27.4 pb−1, respectively. Jets with different areas are reconstructed using the anti-kT algorithm by varying the distance parameter R. The measurements are performed using jets with transverse momenta (pT) greater than 200 GeV and in a pseudorapidity range of |η| < 2. To reveal the medium modification of the jet spectra in PbPb collisions, the properly normalized ratio of spectra from PbPb and pp data is used to extract jet nuclear modification factors as functions of the PbPb collision centrality, pT and, for the first time, as a function of R up to 1.0. For the most central collisions, a strong suppression is observed for high-pT jets reconstructed with all distance parameters, implying that a significant amount of jet energy is scattered to large angles. The dependence of jet suppression on R is expected to be sensitive to both the jet energy loss mechanism and the medium response, and so the data are compared to several modern event generators and analytic calculations. The models considered do not fully reproduce the data. [ABSTRACT FROM AUTHOR]

In this contribution, a recently conducted measurement campaign for indoor millimeter-wave (mm-wave) propagation channels is introduced. A vector network analyzer (VNA)-based channel sounder was exploited to record the channel characteristics at the frequency band from 28–30 GHz. A virtual uniform circular array (UCA) with a radius of 0.25 m was formed using a rotator with 360 steps. Moreover, by taking advantage of fiber-optic technique applied in the channel sounder, measurements at 50 positions were performed from an indoor hall to an indoor corridor along a long pre-defined route. A low-complexity high-resolution propagation estimation (HRPE) algorithm is exploited to estimate the propagation parameters of multipath components (MPCs). Based on the HRPE estimation results, a novel clustering identification and tracking algorithm is proposed to trace clusters. Composite channel characteristics, cluster-level characteristics and dynamic (or birth-death) behaviours of the clusters are investigated, which constitute a dynamic model for the indoor mm-wave channel. [ABSTRACT FROM AUTHOR]

The Sussex MK4 electrical impedance mammography system is especially designed for 3-D breast screening. It aims to diagnose breast cancer at an early stage when it is most treatable. Planar electrodes are employed in this system. The challenge with planar electrodes is the inaccuracy and poor sensitivity in the vertical direction for 3-D imaging. An enhanced image reconstruction algorithm using a duo-mesh method is proposed to improve the vertical accuracy and sensitivity. The novel part of the enhanced image reconstruction algorithm is the correction term. To evaluate the new algorithm, an image processing based error analysis method is presented, which not only can precisely assess the error of the reconstructed image but also locate the center and outline the center and outline the shape of the objects of interest. Although the enhanced image reconstruction algorithm and the image processing based error analysis method are designed for the Sussex MK4 system, they are applicable to all electrical impedance tomography systems, regardless of the hardware design. To validate the enhanced algorithm, performance results from simulations, phantoms and patients are presented. [ABSTRACT FROM AUTHOR]

A new high-resolution virtual spectral imaging technique is able to resolve a closely spaced dominant and low-level sinusoidal signal (power spread of up to 15 dB) in harsh signal-to-noise ratio environments with limited samples where a high-resolution 2-D autoregressive (AR) spectral estimation algorithm failed. This feat is accomplished by applying a 2-D fast Fourier transform to an expanded 2-D measurement data set (which consists of the original measurements extended by vector-extrapolated virtual measurements). The virtual measurement data are created from the original 2-D measurements using an innovative virtual-data vector extrapolation algorithm. A special 2-D AR model is used to model the measurements and then used to extrapolate measurements a vector at a time. Simulations compare our virtual spectral image with a high-resolution 2-D AR spectral image and a spectral image of the truth (the measurements that the extrapolation algorithm is trying to predict). The virtual measurement data are also compared with the true measurement data. We analytically show that the virtual measurements are a function of the true measurements plus some residual error terms. Mean-squared-error simulations show that the extrapolated measurements are well behaved for our problem space and provide a cost example. [ABSTRACT FROM PUBLISHER]

Let A and B be two sets of n resp. m disjoint unit disks in the plane, with m ≥ n. We consider the problem of finding a translation or rigid motion of A that maximizes the total area of overlap with B. The function describing the area of overlap is quite complex, even for combinatorially equivalent translations and, hence, we turn our attention to approximation algorithms. We give deterministic (1 - ∊)-approximation algorithms for translations and for rigid motions, which run in O((nm/∊2) log(m/∊)) and O((n2m2/∊3) log m)) time, respectively. For rigid motions, we can also compute a (1 - ∊)-approximation in O((m2n4/3Δ1/3/∊3) log n log m) time, where Δ is the diameter of set A. Under the condition that the maximum area of overlap is at least a constant fraction of the area of A, we give a probabilistic (1 - ∊)-approximation algorithm for rigid motions that runs in O((m2/∊4) log2(m/∊) log m) time and succeeds with high probability. Our results generalize to the case where A and B consist of possibly intersecting disks of different radii, provided that (i) the ratio of the radii of any two disks in A ∪ B is bounded, and (ii) within each set, the maximum number of disks with a non-empty intersection is bounded. [ABSTRACT FROM AUTHOR]

We consider the rooted orienteering problem: Given a set P of n points in the plane, a starting point r ∊ P, and a length constraint B, one needs to find a path starting from r that visits as many points of P as possible and of length not exceeding B. We present a (1 - ϵ)-approximation algorithm for this problem that runs in nO(1/ϵ) time; the computed path visits at least (1 - ϵ)kopt points of P, where kopt is the number of points visited by an optimal solution. This is the first polynomial time approximation scheme for this problem. The algorithm also works in higher dimensions. [ABSTRACT FROM AUTHOR]